In practice, we implement the method with Valgrind and Fpdebug.
Valgrind is an efficient framework for dynamic analysis
and we use Valgrind to track the calculation results of each instruction.
Fpdebug [1]} is a tool based on Valgrind, which support multi-precision debug.
In addition, Fpdebug calculates with MPFR library,
a C library for multiple-precision floating-point computations with correct rounding.
We complement Fpdebug in purpose of recording original value,
shadow value and realizing reducePrec function and resumePrec function, which mentioned before.
